A054684 Numbers whose sum of digits is odd.

1, 3, 5, 7, 9, 10, 12, 14, 16, 18, 21, 23, 25, 27, 29, 30, 32, 34, 36, 38, 41, 43, 45, 47, 49, 50, 52, 54, 56, 58, 61, 63, 65, 67, 69, 70, 72, 74, 76, 78, 81, 83, 85, 87, 89, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 111, 113, 115, 117, 119, 120, 122, 124, 126, 128, 131

Offset: 1

Author

Odimar Fabeny, Apr 19 2000

Keywords

• nonn
• easy
• base

Comments

Union of A179083 and A179085; A179081(a(n)) = 1. - Reinhard Zumkeller, Jun 28 2010

Equivalently, integers with an odd number of odd digits. - Bernard Schott, Nov 06 2022

Examples

			1, 3, 5, 7, 9, 10(1), 12(3), 14(5), 16(7), 18(9), 21(3) and so on.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Index entries for 10-automatic sequences.
• Index entries for Colombian or self numbers and related sequences

Crossrefs

Cf. A054683, A137233 (number of n-digits terms).

Cf. A356929 (even number of even digits).

A294601 (exactly one odd decimal digit) is a subsequence.

Programs

Maple

[seq(`if`(convert(convert(2*n-1,base,10),`+`)::odd, 2*n-1, 2*n-2), n=1..501)];

Mathematica

Select[Range[200],OddQ[Total[IntegerDigits[#]]]&] (* Harvey P. Dale, Nov 27 2021 *)

PARI

is(n)=my(d=digits(n));sum(i=1,#d,d[i])%2 \\ Charles R Greathouse IV, Aug 09 2013

PARI

isok(m) = sumdigits(m) % 2; \\ Michel Marcus, Nov 06 2022

PARI

a(n) = n=2*(n-1); n + !(sumdigits(n)%2); \\ Kevin Ryde, Nov 07 2022

Python

def ok(n): return sum(map(int, str(n)))&1
print([k for k in range(132) if ok(k)]) # Michael S. Branicky, Nov 06 2022

Formula

a(n) = n * 2 - 1 for the first 5 numbers; a(n) = n * 2 for the second 5 numbers.

From Robert Israel, Jun 27 2017: (Start)

a(n) = 2*n-2 if floor((n-1)/5) is in the sequence, 2*n-1 if not.

G.f. g(x) satisfies g(x) = (1-x)*(1+x+x^2+x^3+x^4)^2*g(x^10)/x^9 + x^2*(2+x^4+3*x^5-x^9+3*x^10)/((1-x)*(1+x^5))^2.

(End)

Extensions

More terms from James Sellers, Apr 19 2000